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Re: Accuracy problem [message #47945 is a reply to message #19921]

Sat, 11 March 2006 03:56

James Kuyper
Messages: 425
Registered: March 2000

Senior Member

David Fanning wrote:
> Juan Arrieta writes:
>
>> I am preparing a simple code to transform between cartesian vectors
>> and Keplerian elements (semimajor axis, inclination, eccentricity, and
>> so forth). This is a simple problem in astrodynamics.
>>
>> At some point in my code, I need to obtain unit vectors. For instance,
>> a line of the code is:
>>
>> U0 = ACOS( (TRANSPOSE(NDVCT) # R) / ( NORM(NDVCT) * NORM(R) ) )
>> % Program caused arithmetic error: Floating illegal operand
>> print,U0
>> NaN
...
> "fancy" programming. I don't know exactly what the problem
> is here, but clearly you need more precision. I'd start by
> doing everything in DOUBLE precision. You don't tell us
> what datatype NDVCT and R are but the NORM function is
> being done as a FLOAT, since you haven't set the DOUBLE
> keyword.
>
> I'd step back a couple of steps before you introduced us
> to the problem and make sure everything is done in double
> precision values. Then, after you have convinced yourself
> you've done everything humanly possible, I think you might
> be justified in confining the arguments to ACOS to the
> proper range:
>
> arg = ACOS(0.0 > expr < 1.0)

Using double precision floating point will help, but even with double
precision, for some sufficiently small value epsilon, any expression
whose mathematically exact result lies between 1.0-epsilon and 1.0 has
a chance of evaluating numerically to a result >1.0, due to roundoff
error. You HAVE to cap ACOS(-1.0 > expr < 1.0) to cope with these
problems. I wouldn't recommend a lower limit of 0.0 unless that's
actually indicated by the nature of your problem. Small negative
arguments to ACOS don't pose the same kind of problem that arguments
slightly greater than 1.0 do.

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[Message index]

		accuracy problems By: J�rg Schliwa on Thu, 27 April 2000 00:00
		Re: Accuracy problem By: kehcheng on Sat, 11 March 2006 22:45
		Re: Accuracy problem By: Juan Arrieta on Sat, 11 March 2006 19:37
		Re: Accuracy problem By: mmeron on Sat, 11 March 2006 16:25
		Re: Accuracy problem By: David Fanning on Sat, 11 March 2006 06:14
		Re: Accuracy problem By: James Kuyper on Sat, 11 March 2006 03:56
		Re: Accuracy problem By: mmeron on Fri, 10 March 2006 22:52
		Re: Accuracy problem By: David Fanning on Fri, 10 March 2006 21:43

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